## Hiroshima Mathematical Journal

### Extremality of quaternionic Jørgensen inequality

#### Abstract

Let $\mathrm{SL}(2,\mathbb{H})$ be the group of $2 × 2$ quaternionic matrices with Dieudonné determinant one. The group $\mathrm{SL}(2,\mathbb{H})$ acts on the five dimensional hyperbolic space by isometries. We investigate extremality of Jørgensen type inequalities in $\mathrm{SL}(2,\mathbb{H})$. Along the way, we derive Jørgensen type inequalities for quaternionic Möbius transformations which extend earlier inequalities obtained by Waterman and Kellerhals.

#### Article information

Source
Hiroshima Math. J., Volume 47, Number 2 (2017), 113-137.

Dates
Revised: 3 August 2016
First available in Project Euclid: 7 July 2017

https://projecteuclid.org/euclid.hmj/1499392822

Digital Object Identifier
doi:10.32917/hmj/1499392822

Mathematical Reviews number (MathSciNet)
MR3679886

Zentralblatt MATH identifier
06775344

#### Citation

Gongopadhyay, Krishnendu; Mukherjee, Abhishek. Extremality of quaternionic Jørgensen inequality. Hiroshima Math. J. 47 (2017), no. 2, 113--137. doi:10.32917/hmj/1499392822. https://projecteuclid.org/euclid.hmj/1499392822